Problem with seamlessly fitting objects together
What's going on is you need to actually separate the geometry before you add those faces.  Bisect just adds an edge loop, it doesn't actually separate the geometry.  So as far as Blender knows, those two pieces are still one surface, and then adding those faces in the middle is creating a kind of geometry that simply doesn't work; this specific problem is called &quot;internal faces.&quot;  Internal faces should always be avoided, because 3D modeling software simply isn't built to handle such geometry; for example, creating these weird shading artifacts around the edges of the internal faces.
So, make sure you actually separate the geometry before you add those faces.  You can do this by selecting the bisecting edge loop and pressing Alt-M and choosing &quot;Faces by Edges,&quot; or you can select all the faces on one side of the edge loop and press Y.  Both produce the same result.  You can make sure everything really is separated by hovering your cursor over one of the sections and pressing L, which selects all the geometry that is connected to that section.  If it only selects the individual section, you're good to go.  If it selects the whole thing, it still isn't separated.
After you do the separation, you'll have to create those inside faces for each piece.  Once you do this, the smooth shading will inevitably show where the cracks are; you can counter this by toggling on &quot;Auto Smooth&quot;, which I show how to find in this screenshot.